Questions: The average human generates approximately his or her weight in ATP every day. A resting person uses about 25% of this in ion transport-mostly via the Na^+ - K^+ ATPase. Part A About how many grams of Na^+ will a sedentary 90-kg person pump across membranes in a day? Express your answer in grams to two significant figures. Part B About how many grams of K^+ will a sedentary 90 - kg person pump across membranes in a day?

To answer the questions, we need to understand the relationship between ATP usage and ion transport, specifically for sodium (\(\mathrm{Na}^+\)) and potassium (\(\mathrm{K}^+\)) ions.

1. Determine the total ATP usage per day:

   • A 90-kg person generates approximately their weight in ATP every day.
   • Therefore, a 90-kg person generates 90 kg of ATP per day.

2. Calculate the ATP used for ion transport:

   • A resting person uses about 25% of their ATP for ion transport.
   • \( 25\% \) of 90 kg = \( 0.25 \times 90 \, \text{kg} = 22.5 \, \text{kg} \) of ATP.

3. Estimate the amount of \(\mathrm{Na}^+\) transported:

   • The \(\mathrm{Na}^+-\mathrm{K}^+\) ATPase pumps 3 \(\mathrm{Na}^+\) ions out of the cell for every ATP molecule hydrolyzed.
   • The molar mass of ATP is approximately 507 g/mol.
   • The molar mass of \(\mathrm{Na}^+\) is approximately 23 g/mol.

4. Convert the mass of ATP to moles:

   • \( 22.5 \, \text{kg} = 22500 \, \text{g} \)
   • Moles of ATP = \( \frac{22500 \, \text{g}}{507 \, \text{g/mol}} \approx 44.4 \, \text{mol} \)

5. Calculate the moles of \(\mathrm{Na}^+\) transported:

   • Since 1 mole of ATP pumps 3 moles of \(\mathrm{Na}^+\),
   • Moles of \(\mathrm{Na}^+\) = \( 3 \times 44.4 \, \text{mol} = 133.2 \, \text{mol} \)

6. Convert moles of \(\mathrm{Na}^+\) to grams:

   • Mass of \(\mathrm{Na}^+\) = \( 133.2 \, \text{mol} \times 23 \, \text{g/mol} \approx 3063.6 \, \text{g} \)

   Therefore, the amount of \(\mathrm{Na}^+\) pumped across membranes in a day is approximately 3100 grams (to two significant figures).

1. Estimate the amount of \(\mathrm{K}^+\) transported:

   • The \(\mathrm{Na}^+-\mathrm{K}^+\) ATPase pumps 2 \(\mathrm{K}^+\) ions into the cell for every ATP molecule hydrolyzed.
   • The molar mass of \(\mathrm{K}^+\) is approximately 39 g/mol.

2. Calculate the moles of \(\mathrm{K}^+\) transported:

   • Moles of \(\mathrm{K}^+\) = \( 2 \times 44.4 \, \text{mol} = 88.8 \, \text{mol} \)

3. Convert moles of \(\mathrm{K}^+\) to grams:

   • Mass of \(\mathrm{K}^+\) = \( 88.8 \, \text{mol} \times 39 \, \text{g/mol} \approx 3463.2 \, \text{g} \)

   Therefore, the amount of \(\mathrm{K}^+\) pumped across membranes in a day is approximately 3500 grams (to two significant figures).

• Part A: A sedentary 90-kg person pumps approximately 3100 grams of \(\mathrm{Na}^+\) across membranes in a day.
• Part B: A sedentary 90-kg person pumps approximately 3500 grams of \(\mathrm{K}^+\) across membranes in a day.